The invention disclosed and claimed herein generally pertains to an improved technique for spatially encoding magnetic resonance (MR) image data. More particularly, the invention pertains to a spatial encoding technique wherein time dependence is deliberately introduced in the phase encoding direction, as well as in the readout direction. Even more particularly, the invention pertains to a technique of the above type wherein time dependence is the same in both the phase encoding and readout directions, in order to provide diagonally directed virtual frequency encoding.
As is well known in the MR imaging arts, conventional two-dimensional Fourier Transform (2DFT) MR imaging is characterized by a phase encoding direction and a frequency encoding, or readout direction. More particularly, in conventional MR techniques such as spin warp and spin echo, an RF excitation pulse is applied to a region of interest in an imaging subject, to produce an MR data signal representing structure therein. A phase encoding gradient and a readout gradient are likewise applied to the region of interest, and the data signal is sampled during the readout gradient and a concurrent data acquisition window. If the readout gradient field is directed along the spatial X-axis of the associated MR imaging system, respective data sample points will be located in k-space at different positions k.sub.x along the k.sub.x -axis. The data points acquired from the MR signal collectively comprise a view. Thereafter, further sets of RF excitation, phase encoding, and readout gradient pulses are applied to the region of interest to produce successive MR data signals, and to acquire successive views respectively corresponding thereto. Thus, each view is associated with a phase encoding gradient of different amplitude. If the phase encoding gradient is directed along the spatial Y-axis, respective views will be identified in k-space by corresponding positions k.sub.y along the k.sub.y -axis.
A conventional spin warp imaging sequence, illustrating the above features, is shown in FIG. 1. Therein, G.sub.z is a slice select gradient, G.sub.x and G.sub.y comprise the readout and phase encoding gradients, respectively, and an MR data signal (not shown) is sampled over the data acquisition window. Generally, if the MR data signal at each location (x, y) in the region of interest is m(x, y), the signal S for an entire 2DFT image reconstruction can be expressed as follows: ##EQU1##
It will be readily apparent that a finite, non-zero amount of time is needed to acquire a set of data points from an MR signal during the data acquisition window. In conventional 2DFT MR imaging, time may be defined as t=t.sub.TE +.DELTA.t.sub.kx,ky, where the term t.sub.TE represents the time over which a static phase offset is accrued, due to offset of the gradient recalled echo from the RF excitation pulse (or for a spin echo sequence, from the RF-refocused echo). .DELTA.t.sub.kx,ky represents the time offset from t.sub.TE at which each k.sub.x, k.sub.y signal is acquired. For the conventional 2DFT imaging method, the k-space time dependence .DELTA.t.sub.kx, ky may be expressed independently for each axis. As is well known, .DELTA.t.sub.kx, the time at which data point k.sub.x is acquired as shown in FIG. 1, is .DELTA.t.sub.kx =k.sub.x /.gamma.G.sub.x. Thus, data acquisition along the k.sub.x -axis, i.e., in the readout direction, proceeds as a linear function of time. Moreover, data acquisition for each successive phase encoding gradient always commences at the same time following the RF signal, i.e., at t.sub.TE. As a result, .DELTA.t.sub.ky =0. Accordingly, the only time dependence in the conventional 2DFT MR imaging is a linear time dependence, along a single axis (e.g.,. the k.sub.x -axis).
It is to be understood that the expression for the MR signal S, as set forth in Equation (1), assumes that all the phase shifts experienced by respective sampled data points result from the spatial encoding process as expressed in the term e.sup.-i(kx x+ky y). Failure to take into account a condition known as off resonance, commonly due to phenomena such as chemical shift or B.sub.0 inhomogeneity, leads to artifacts in MR reconstruction from the acquired data, most notably displacement artifacts in the frequency encoding direction (e.g., the x direction). Accordingly, a more complete form of the signal equation for conventional 2DFT imaging, which captures the effect of off resonance as an additional signal phase term .DELTA..phi.=.DELTA..omega.t, is as follows: ##EQU2##
In Equation (2), S(t) is a complex data point acquired at the time t, k.sub.x and k.sub.y are the time integrals of the gradients G.sub.x and G.sub.y, respectively, and .DELTA..omega. is the angular frequency offset of spins at a given (x, y) location.
The off resonance distortion represented by .DELTA..omega. results in geometric distortion in an FT reconstructed image. More particularly, as further developed hereinafter, the off resonance distortion causes MR signal information acquired at a location x to be shifted to a position x' in the image, where x'=x+.DELTA..omega./.gamma.G.sub.x. However, because of the time independence of conventional 2DFT imaging in the phase encoding direction, as described above, the image will not be distorted in such direction (e.g., the y direction). In the past, this absence of artifact in the y direction and simple displacement artifact in the x direction due to off resonance was a principal reason for the rapid and widespread adoption of the spin-warp method as the spatial encoding method of choice in MR imaging.
As is well known, swapping the phase and frequency encoding directions is a common practice in MR imaging, to reduce aliasing and also to alter the appearance of motion or flow artifacts. Thus, in accordance with these methods, an initial set of MR data is acquired with the frequency encoding direction oriented, for example, along the X-axis and the phase encoding direction oriented along the Y-axis. Thereafter, a second data set is acquired with the frequency and phase encoding directions swapped. It will be readily apparent that swapping the phase and frequency encoding directions also swaps or changes the direction of off resonance distortion, which necessarily follows the frequency encoding axis. It is also apparent that direct comparison or combination of such images, as for example by averaging or by subtraction will be imperfect in regions affected by off resonance distortion. This has tended to limit the usefulness of such combination or comparison techniques.